CN106991204A - Modification to affined asymmetric subdivided meshes - Google Patents
Modification to affined asymmetric subdivided meshes Download PDFInfo
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- CN106991204A CN106991204A CN201611110101.XA CN201611110101A CN106991204A CN 106991204 A CN106991204 A CN 106991204A CN 201611110101 A CN201611110101 A CN 201611110101A CN 106991204 A CN106991204 A CN 106991204A
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
- G06F30/23—Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2111/00—Details relating to CAD techniques
- G06F2111/04—Constraint-based CAD
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2111/00—Details relating to CAD techniques
- G06F2111/20—Configuration CAD, e.g. designing by assembling or positioning modules selected from libraries of predesigned modules
Abstract
Embodiment, which is provided, to be used to change the method and system that the finite element mesh of threedimensional model is represented.The symmetry constraint of finite element mesh is defined according to the method for embodiment, wherein finite element mesh is the expression of main body 3D models, and symmetry constraint includes two asymmetric areas of the finite element mesh symmetrically to be changed.Then, at least one element of corresponding finite element of the identification between two asymmetric areas and the corresponding finite element to being recognized performs manipulation.As response, manipulation is symmetrically performed on two or more corresponding finite elements for being recognized, wherein two or more finite elements are identified as corresponding at least one finite element.In such embodiments, symmetrically performing manipulation causes two asymmetric areas symmetrically to be changed, and represents the symmetrical modification in main body 3D models.
Description
Background technology
Embodiments of the invention relate generally to the field of computer program and system, and more particularly to product design
With the field of simulation.The multiple existing products and mould of design and the simulation of component for part or part are commercially provided
Plan system.Such system typically uses CAD (CAD) and computer-aided engineering (CAE) program.These are
System allows the complex three-dimensional model of the component of user's construction, manipulation and simulated object or object.These CAD and CAE systems because
This is in the expression for providing modeled object using edge or line in some cases with face.Can (example in various manners
Such as, non-uniform rational B-spline (NURBS)) represent line, edge, face or polygon.
These CAD systems manage the part or the component of part of modeled object, and it is mainly the specification of geometry.
Specifically, cad file includes specification, and geometry is produced by specification.According to geometry, expression is produced.Specification, geometry knot
Structure and expression can be stored in single cad file or multiple cad files.CAD system includes being used to represent through building to designer
The graphical tool of the object of mould；These instruments are exclusively used in the display of complex object.For example, component can include thousands of parts.
The appearance of CAD and CAE systems allows the various expression possibilities of object.Represent it is limited as one
Elementary analysis (FEA) model.Term " FEA model, finite element model (FEM), finite element mesh and grid " is herein
It is interchangeably used.FEM typicallys represent CAD model, and therefore can represent one or more parts or whole component.FEM
It is the system for the point for being referred to as node for being interconnected to produce the grid for being referred to as grid.Therefore, FEM can by summit, edge and/
Or face is represented.FEM (including summit, edge and face) can be to cause FEM to have its fundamental objects for representing or Properties of Objects
Mode be programmed.It can store extra information to improve description for FEM each entity.For example, finite element model
Architectural characteristic can be programmed to have according to principle as known in the art, for example quality, the weight of its object represented
And rigidity.In addition, FEM can include information, such as attraction of the various entities of FEM and the mark for identification.As FEM or such as
When the other such objects being known in the art represent to be programmed in this way, it can be used for performing its expression
Object simulation.For example, FEM can be used to indicate that the interior cabin of vehicle, the acoustic fluid around structure and any amount of
Real-world objects.In addition, CAD and CAE systems are used for model engineering system together with FEM.For example, CAE systems can be with
Noise and vibration for simulating vehicle.
The content of the invention
Embodiments of the invention are provided for changing the method and system that the finite element mesh of three-dimensional (3D) model is represented.
Embodiments of the invention are started by the way that the symmetry constraint of finite element mesh is defined by the user, finite element mesh
The expression of main body (subject) 3D models, and symmetry constraint include symmetrically being changed the two of finite element mesh
Individual asymmetric area.Then, such embodiment recognizes the corresponding finite element between two asymmetric areas.Then, by with
Family performs manipulation at least one element of the corresponding finite element recognized in two asymmetric areas.And then, at second
Or manipulation is symmetrically performed on multiple recognized corresponding finite elements, two or more finite elements are identified as correspondence
In at least one finite element.According to embodiment, symmetrically performing to manipulate causes two asymmetric area's quilts of finite element mesh
Symmetrically change, and thereby represent the symmetrical modification in main body 3D models.
In embodiment, recognize that corresponding finite element recognizes symmetrical edge, summit and the face in two asymmetric areas.For
In the embodiment in generation, symmetrically performing to manipulate includes determining Local Symmetric plane, and the Local Symmetric plane is had by least one
It is that the barycenter of limit element and two or more finite elements is defined and perpendicular to by least one finite element and second or
The direction that multiple finite elements are defined.In addition, according to such embodiment, symmetry transformation is calculated using Local Symmetric plane,
And calculated symmetry transformation is performed on two or more finite elements.
In embodiment, defining symmetry constraint includes at least one in following operation：Recognize first group of face through connection
With second group of face through connection, identification plane and one group of face through connection recognize one group of face, and identification plane.In another reality
Apply in example, symmetry constraint is only applied to the subdivision of finite element mesh.Also further, in embodiment, using corresponding
Uniquely tagged recognizes the element in two asymmetric areas of finite element mesh.
In alternate embodiments, defining symmetry constraint includes determining the separation shape between two asymmetric areas.
In such embodiment, separation shape can be plane.In addition, in another embodiment, identification two asymmetric areas it
Between corresponding finite element in using separation shape.
The alternative embodiment of the present invention is related to for changing the computer system that the finite element mesh of 3D models is represented.
Such system includes processor and memory, and memory has the computer generation code instruction being stored thereon, wherein processor
It is configured as system is realized various embodiments specifically described herein with the memory with computer generation code instruction.One this
In the embodiment of sample, processor and the memory with computer generation code instruction make system：In response to the first customer interaction,
Define the symmetry constraint of finite element mesh, wherein finite element mesh is the expression of main body 3D models, and wherein it is symmetrical about
Beam includes two asymmetric areas of the finite element mesh symmetrically to be changed；And recognize between two asymmetric areas
Corresponding finite element.In addition, in such computer system embodiment, processor and depositing with computer generation code instruction
Reservoir also makes system in response to second user reciprocation in the corresponding finite element recognized in two asymmetric areas
At least one perform manipulation, and symmetrically held on two or more corresponding finite elements for being recognized as response
Row is manipulated, wherein two or more finite elements are identified as corresponding at least one finite element.According to embodiment, symmetrically
Ground, which performs to manipulate, causes two asymmetric areas of finite element mesh symmetrically to be changed, and manipulates in expression main body 3D models
Symmetrical modification.
System identification is also made according to the embodiment of computer system, processor and the memory with computer generation code instruction
Symmetrical edge, summit and the face in Liang Ge areas.In addition, according to another embodiment, in symmetrically performing and manipulating, processor and have
The memory of computer generation code instruction also makes system determine Local Symmetric plane, and the Local Symmetric plane is limited by least one
The barycenter definition of element and two or more finite elements and perpendicular to by least one finite element and the two or more
The direction that finite element is defined.In addition, in such embodiments, making computer system and behaviour being calculated using Local Symmetric plane
Vertical symmetry transformation, and the calculated symmetry transformation of execution on two or more finite elements.
The alternative embodiment of computer system is configured as realizing function, and wherein symmetry constraint is only applied to finite element
The subdivision of grid.According to another embodiment, in symmetry constraint is defined, processor and the storage with computer generation code instruction
Device is additionally configured at least one in making to list under system identification：First group of face through connection and second group of face through connection,
Plane and one group of face through connection, one group of face and plane.Also further, the embodiment of computer system is utilized accordingly only
The element in one two asymmetric areas for marking to recognize finite element mesh.
In another embodiment, processor and the memory with computer generation code instruction make computer system in definition pair
Claim to determine the separation shape between two asymmetric areas in constraint.And then, it is non-right at two recognizing according to another embodiment
Claim to use separation shape during the corresponding finite element between area.In addition, in embodiment, separation shape is plane.
Another embodiment of the present invention is related to for changing the cloud computing embodiment party that the finite element mesh of 3D models is represented
Formula.Such embodiment is related to the computer program performed in the communication of across a network and one or more clients by server
Product, wherein computer program product include computer-readable medium.In such embodiments, computer-readable medium includes
Programmed instruction, it causes when being executed by a processor：The symmetry constraint of finite element mesh is defined, finite element mesh is main body
The expression of 3D models, and symmetry constraint includes two asymmetric areas of the finite element mesh symmetrically to be changed；And
Recognize the corresponding finite element between two asymmetric areas.In addition, in such embodiments, programmed instruction is when by handling
Device also causes when performing：Behaviour is performed at least one element in the corresponding finite element recognized in two asymmetric areas
It is vertical.And then, performed programmed instruction causes：Symmetrically performed on two or more corresponding finite elements for being recognized
Manipulate, wherein two or more finite elements are identified as corresponding at least one finite element.In such embodiments,
Symmetrically performing to manipulate causes two asymmetric areas of finite element mesh symmetrically to be changed, and represents in main body 3D models
Symmetrical modification.
The application be related to the priority date of the application EPO and submitted by same applicant, it is entitled
" TOPOLOGICAL CHANGE IN A CONSTRAINED ASYMMETRICAL SUBDIVISION MESH " and with phase
The application of same inventor, its entire teaching is incorporated herein by reference.Among other examples, to two of the application
The manipulation for the corresponding finite element that at least one of asymmetric area is recognized can be such as the execution described in related application
Topology manipulation, and the two applications can utilize for defining symmetry constraint, the corresponding finite element of identification and right in addition
Ground is claimed to perform the same or similar method manipulated.
Brief description of the drawings
Foregoing teachings are by the following more specifically description of the exemplary embodiment according to the present invention it is clear that such as existing
Shown in accompanying drawing, wherein similar reference refers to identical part in all different views.Accompanying drawing might not
It is proportionally, conversely it is emphasised that explanation embodiments of the invention.
Fig. 1 depicts the surface that can be utilized in embodiment and finite element mesh.
Fig. 2 shows a part for the grid by symmetry constraint of principle according to an embodiment of the invention.
Fig. 3 depict can utilize in one or more embodiments there is having for disparity and asymmetric topology structure
Limit element grid.
Fig. 4 shows the exemplary functions provided by embodiment, wherein with mobile grid and symmetry constraint can be maintained.
Fig. 5 depicts the function of being provided by the exemplary embodiment of the present invention.
Fig. 6 shows the stream for the computer based method for describing the modification finite element mesh according to the principle of embodiment
Cheng Tu.
Fig. 7 shows the symmetry constraint defined according to embodiment.
Fig. 8 depicts the finite element mesh of the symmetry constraint including being defined according to the principle of example embodiment.
Fig. 9 is the finite element mesh with the symmetry constraint area defined according to the method for embodiment.
Figure 10 depicts the finite element mesh symmetrically constrained according to embodiment.
The method that Figure 11 shows the finite element mesh that analysis can be utilized in embodiment.
Figure 12 depicts the finite element mesh with the uniquely tagged system that can be utilized in an embodiment of the present invention.
Figure 13 depicts the example using the symmetry transformation according to exemplary embodiment.
Figure 14 is depicted is constraining finite element mesh when creating and after modification according to exemplary embodiment
Finite element mesh.
Figure 15 depicts the exemplary embodiment of definition constraint.
Figure 16 A-C show the grid that can be symmetrically performed using defined constraint with embodiments in accordance with the present invention
Modification.
Figure 17 is the flow chart for defining the computer based method according to the symmetry constraint of embodiment.
Figure 18 is the computer based method for changing grid using symmetry constraint according to the principle of exemplary embodiment
Flow chart.
Figure 19 is the simplified block diagram for being used to change the computer system of finite element mesh according to embodiment.
Figure 20 can be achieved on the simplification figure of the computer network environment of embodiments of the invention.
Embodiment
The exemplary embodiment of the present invention is described as follows.
Embodiments of the invention are related to completely by representing the subdivision surface that the subdivided meshes of 3D models are defined.More specifically,
The concept of embodiment processing " symmetric shape ", it can be the standard feature in CAD software.Embodiment is provided for so
Function more effective way and system.
As mentioned in this article, embodiments of the invention are related to CAD and 3D models.Fig. 1 is depicted to be defined by grid 101
A surface 100.Designer for example can increase efficiency using embodiments of the invention, while changing grid 101.Cause
This, effectively reflects that the expectation to surface 100 is changed.
Many manufactured objects are symmetrical or with symmetrical some parts, such as screen and television set, phone, head
Headset, mug, automotive seat etc..In addition, many real-world objects can be in itself or part thereof asymmetrical, but
It is probably still desirable symmetrically to produce change to these parts.Therefore, to maintaining to represent that real-world objects have
The constraint for limiting the symmetry characteristic of element grid is the useful function in CAD software.Embodiments of the invention can be used for increase
Efficiency in the design and modeling of substantially any object, because most of object, which is included, can utilize embodiments of the invention
Principle is come the locally or globally symmetrically or non-symmetrically part that constrains.For example, can the groove with the thumb for user meter
Calculation machine mouse, with for the television set of loudspeaker or the nonsymmetry boundary of button position, mobile phone and with two not
With in the design of a pair of scissors of the finger hole of size use embodiments of the invention.Described method and system herein
In example, 3D models represent headphone, and symmetry constraint is related to two earphones, and manipulating is held by CAD design person
Go to change the shape of any one in two earphones and/or the design operation of positioning.In another embodiment, 3D models are represented
The back seat of automobile, and whole seat is by symmetry constraint.Therefore, can when the left headrest to such as seat is changed
Effectively to perform this change to right headrest.
The major way of process problem is to provide from common subdivided meshes and plane and builds or see whole in the prior art
The mode of individual Symmetric Mesh (that is, full symmetric grid is created from original mesh).But, although such existing solution
User is allowed to create complete Symmetric Mesh, it means that on the topology and be geometrically symmetrical, this is from man-machine work
The maximally effective solution of the design to manufactured object mentioned above is not necessarily from the point of view of Cheng Xue viewpoints.Therefore carry
Go out a kind of method and system as an improvement, this method and system allow user：Only the subdivision of grid is defined as symmetrically；Repair
Change the right side or left side in symmetrical area；With some disparities with asymmetric topology structure；Towards selected in different places
Face mobile grid is allocated without destroying symmetry constraint；And/or improve or simplify subdivision surface and keep symmetry constraint as far as possible.
Among other functions, existing solution does not provide above-mentioned function.
As described above, being whole subdivided meshes and the existing solution of planar design.Embodiments of the invention are utilized
Restrained symmetrical area inside subdivided meshes, and maintain this to constrain in the whole modification of grid.Which improve man-machine work
Cheng Xue.
Embodiments of the invention provide many functions that existing method is not supported.For example, embodiments of the invention are only permitted
Perhaps the subdivision of grid is confined to symmetrically.Fig. 2 shows grid 220, wherein only part 221 is confined on plane
224 be symmetrical.In addition, embodiment realizes function, wherein the right side or left side in symmetrical area can be changed.This function allows
The left side 222 and/or right side 223 in such as symmetrical area 221 are changed.In addition, as shown in Figure 3, embodiments of the invention branch
Hold using asymmetric topology structure to create disparity.In figure 3, finite element mesh 331 and 332 is on the topology
With, but be geometrically different.In addition to other reasons, grid 332 is additionally included in and corresponding edge 335 and 336
Edge 333 and 334 under different angles.Therefore, grid 331 and 332 itself is pair on the topology on 339 and 340
Claim, but they on those identical planes be not geometrically symmetrical.
Further embodiment provides the ability without destroying symmetry constraint for mobile grid.Fig. 4, which is depicted, to be confined to
It is the grid 440 at symmetrical first position 442a towards plane 441.Then, grid 440 is moved into place relative to plane 441
Put 442b and changed (difference shown in from 443a to 443b).The symmetrical of grid 440 is defined rigorously by using plane 441
Constraint, user always can change shape using constraint, and towards selected plane by Grid Mobile to different places
Do not destroy symmetry constraint.Embodiments of the invention can realize this by not considering panel data after the definition of constraint.
This solution allows to maintain symmetric manipulator for all elements of grid to be moved.This is also achieved to asymmetric grid
Manipulation.For example, in Fig. 4, grid 440 is asymmetrical on plane 441, and therefore by not utilizing panel data,
After symmetry constraint is defined, grid 440 can be moved relative to plane 441, as shown in frame 442b, and can be with
Maintain symmetry constraint.According to embodiment, this can lead to after grid 440 is by movement and/or when making modification to grid 440
Cross and determine new symmetrical plane to realize.
Further embodiment provides the function for the finite element mesh that improve or simplify, while being always maintained at symmetry constraint
For modification as much as possible.Fig. 5 depicts grid 550 and the grid 551 changed, wherein by required various modifications to obtain
To the grid 551 changed, symmetry constraint is maintained.Although embodiment maintains symmetry constraint by much changing, in replacement
In embodiment, there is the limitation of the modification to that can be performed, while maintaining symmetry constraint.For example, in specific condition (for example
The modification of strong and destructive topological structure is performed) embodiment in, it may be difficult to recognize the profile in symmetrical area.In embodiment
In there is provided function is with editor's symmetry constraint when constraint can not be maintained and/or redefines symmetry constraint.
Known trial is not carried out to define, store and maintain such " symmetry constraint " to be able to carry out being previously noted
Function.In an embodiment of the present invention, symmetrical area is defined by being verified and creating with grid sheet.Constraint is logical
The integrated quilt " storage " crossed in surface mesh, and transmitted and replicated by streaming, to cause surface mesh to be no longer simple
Basic grid, and in addition, by performing all operations on the both sides of grid (for example, vertex translations, face extruding and face are moved
Except) come maintain constraint.This is successfully handled before the CAD or other softwares without known to.
Fig. 6 be according to an embodiment of the invention principle be used to changing that the finite element meshes of 3D models represents based on
The flow chart of computer method 660.Equation 660 is started by defining the symmetry constraint of finite element mesh, wherein symmetrically
Constraint is included in two asymmetric areas that step 661 is symmetrically changed.According to embodiment, two asymmetric areas include a networking
Lattice element, such as face, summit and/or edge.Various methods can be used (for example, first group of face and second through connection of identification
Face of the group through connection, identification plane and one group of face through connection, one group of face of identification and identification plane) define symmetry constraint.This
Outside, the embodiment of computer implemented method 660 can utilize any method for defining symmetry constraint specifically described herein
Or the combination of method.It is described herein below in relation to Fig. 7-10 and 17 on for defining what can be utilized in method 660
The other details of the method for symmetry constraint.For example, in embodiment, agent grid is shown on a monitor, and user makes
Select to include face, the edge of the grid in symmetrical area with mouse, touch-screen or any user/interfacial process as known in the art
And/or summit.In another embodiment, can be by selecting symmetrical plane to recognize symmetry constraint.In addition, symmetry constraint can
To be defined to include any part of grid, such as some subdivisions of whole grid or finite element mesh.
As described above, the definition of method 660 include the two asymmetric areas symmetrically to be changed it is symmetrical about
Beam.The embodiment of method 660 can be used for changing various finite element meshes, wherein such as grid is asymmetrical, but need
Symmetrically perform modification.The example of such grid is depicted and is described above in fig. 2.Wherein grid 220 includes
Symmetry constraint 221, it includes two asymmetric areas 222 and 223.According to embodiment, defining symmetry constraint in step 661 is included really
It is scheduled on the separation shape between two asymmetric areas.In such embodiments, separation shape can be it is desired it is any so
Shape.In addition, according to embodiment, separation shape can be default shape, such as the plane between the two areas.Also enter one
Step ground, in another embodiment, separation shape are identified as being located at the barycenter in two asymmetric areas and perpendicular at the two
The plane in the direction between area.Among other examples, can use each area closed contour barycenter come recognize this two
Direction between individual area.In such an example, the section between that two barycenter can be defined between the two areas
Direction.Exemplary separation shape 224 is depicted in fig. 2.In addition, although the definition of method 660 includes pair in two asymmetric areas
Claim constraint, embodiments of the invention are not so limited, and in alternate embodiments, symmetry constraint can be right including two
Claim area.
After step 661 defines symmetry constraint, method 660 continues and recognized between two symmetrical areas in step 662
Corresponding finite element.According to embodiment, recognize that corresponding element includes symmetrical edge, summit and the face in identification Liang Ge areas.
The example of corresponding finite element for example on Figure 12 and Figure 13 whole descriptions.For example, describe in fig. 12 summit (7,
13) the corresponding element that can be recognized during the step 662 of method 660 can be all considered with (6,16) and face (7,13).
Similarly, described summit (1331,1333) herein describe in fig. 13 and following can similarly be identified as pair
Answer.In addition, according to embodiment, step 662 recognize corresponding finite element can include identification two asymmetric areas it
Between all such corresponding elements, or alternatively any amount of corresponding element.In embodiment, propagated using neighbour
Method (such as below in relation to Figure 11 in method described herein) is in the corresponding element of step 662 automatic identification.Also further,
In embodiment, corresponding finite element can be only recognized in response to manipulating (i.e. for example, after being moved on summit), then may be used
To recognize corresponding symmetrical summit.In another embodiment of method 660, when what is determined when step 661 defines symmetric shape
Separation shape can be used for recognizing the corresponding element between Liang Ge areas in step 662.For example, defined separation shape is used
In the two areas of identification, and principle specifically described herein is used, the corresponding element in the two areas can be recognized.
The another embodiment of computer based method 660 is to each element by defined constraint using accordingly
Uniquely tagged.These uniquely taggeds and then corresponding finite element that can be in step 662 in identification between two asymmetric areas
Used when plain.The other details on uniquely tagged is described herein below in relation to Figure 12.
Define symmetry constraint and after step 662 recognizes corresponding finite element in step 661, method 660 by
Step 663 performs the manipulation for the corresponding finite element for recognizing at least one of two asymmetric areas to continue.According to reality
Example is applied, can be inputted in response to user or be ordered and perform manipulation.It can be repaiied with reference to the various of topological structure for not changing grid
Change to use embodiments of the invention.This can by by it is all it is such manipulate as one or more summits " movement " come
Realize.Exemplary manipulation includes translation, rotation, proportional zoom, stretching, projection and putting down along local normal and along edge
Move.Further embodiment realizes summit, face and edge movement.Also further, another embodiment provide for change grid with
Closer to the function of the geometric object of its expression.
In response to the manipulation in step 663, manipulate and then in step 664 in the two or more corresponding having of being recognized
Symmetrically it is performed on limit element.In such embodiments, two or more finite elements are limited corresponding at least one
Element, performs the manipulation in step 663 at least one finite element.In other words, manipulation is performed on such as summit
Afterwards, symmetrically manipulation is performed automatically on corresponding summit in other asymmetric areas.The example of such function is in fig. 13
It is depicted and is described herein lower.Step 664 symmetrically perform manipulation cause two of finite element mesh it is non-right
Area is claimed asymmetricly to be changed.In addition, non-right in step 663 and 664 such modification can represent main body 3D models
Claim modification.
In the embodiment of method 660, symmetrically performing to manipulate in step 664 includes determining Local Symmetric plane, the office
Portion's symmetrical plane is defined by the barycenter of at least one finite element and two or more finite elements and perpendicular to by least one
The direction that individual finite element and two or more finite elements are defined.In addition, such embodiment uses Local Symmetric plane
To calculate the symmetry transformation of manipulation, and and then the calculated symmetry transformation of execution on two or more finite elements.
In exemplary embodiment, calculate and perform definite symmetry transformation, if for example, summit moves to left 1 centimetre, it is corresponding
Summit moves to right 1 centimetre.In another embodiment, calculate and perform transformation of scale.If for example, 10 cm side edges are drawn
2 centimetres are stretched, then corresponding edge is also stretched the 20% of its length.It is described herein below in relation to Figure 13 on calculating pair
Claim the other details of conversion.In embodiment, (for example, motion is symmetrical) is manipulated opposite with position.By this way, exist
Symmetric manipulator is performed in asymmetric area without damaging asymmetry.
According to the embodiment of method 660, finite element mesh is the expression of 3D models.As described herein, 3D moulds
Type and thus represent that the finite element model of same target can represent any kind of real-world objects, such as automobile,
Phone and sports equipment etc..Finite element model can be programmed to have architectural characteristic according to principle as known in the art,
Such as quality and rigidity of its object represented.Therefore, the embodiment of method 660 can be used for improving in such real world
Efficiency in the design of object, wherein expecting symmetrical modification.
Embodiments of the invention can be utilized, so that grid is by any amount of symmetry constraint.Therefore, symmetry constraint
Can be accumulated as the part of grid, thus by some to finite element mesh symmetrically perform manipulation come for
User increases design efficiency.In addition, the embodiment of method 660 can be used for while manipulating multiple elements of finite element mesh.
For example, some edges can be moved, and the principle of embodiments described herein can be then used symmetrically to move another
Each corresponding edge on side.In addition, the exemplary embodiment of the present invention is ignored in the case of being additionally may included in suitably
The function of defined constraint.For example, in the case of multiple elements that user's selection is included in two asymmetric areas, can
To determine design idea, in order to ignore symmetry constraint when making change to element simultaneously in the two asymmetric areas.This
May be necessary in the case where such as user moves whole grid.
Define and store according to principle specifically described herein constraint provide mesh modification in most cases again
Construct the ability of two parts of the grid suffered restraints.In addition, method described herein also assure each modification (cutting,
Extruding, subdivision, hypotenuse cutting etc.) after right hand edge and left hand edge profile reconfigure.
Embodiment can use various techniques to define symmetry constraint.A kind of such method utilizes to have to be worked as in one group of face
In the automatic calculating of right element and left element pair define symmetry constraint.Other embodiments, which are provided, makes user define institute in couples
The mode of the element of constraint.A kind of illustrative methods that can be utilized in embodiment be using two of the face through connection individually
Group defines symmetry constraint.In such embodiments, can be symmetrical on the plane with automatic detection plane, the two groups
's.Fig. 7 depicts the symmetry constraint on the grid 770 defined by the left side group in face 771 and the right group in face 772.So
Example in, user can select the face 771 and 772 of two groups or select one of the group 771 or 772 in face, to define
Symmetry constraint.In this illustration, median plane 773 and 774 does not suffer restraints.In addition, in such an example, can for example lead to
Cross the barycenter calculated between left set of 771 and right group 772 and consider that automatic identification is carried out in the direction between two groups of faces 771 and 772
Plane 775, the left set of in face 771 and right group of face 772 are symmetrical on plane 775.In such an example, the matter calculated
The heart recognizes midpoint between this two groups of faces, and then symmetrical plane is identified as comprising barycenter and is orthogonal to (i.e. perpendicular to)
The plane in the direction between Liang Ge areas.Fig. 8 shows another exemplary embodiment, wherein symmetry constraint by two of face individually
Group definition.Symmetry constraint on grid 880 includes independent group of face 881 and 882, and each group includes five faces.Can with
Above-mentioned example embodiment depicted in figure 7 similarly automatically determines plane 885, and group 881 and 882 is on plane 885
It is symmetrical.
Fig. 9 shows the grid 990 with the symmetry constraint defined according to the principle of another embodiment.Retouched in fig .9
In the embodiment painted, constraint is defined using one group of face 991.In such embodiments, the half 992 in this group of face 991 is located at
On the side of plane 994, and this group 991 second half 993 be located at plane 994 opposite side on.In this exemplary implementation
In example, in the case where constraint is defined by single group face, plane 994 can be automatically recognized again.
In addition, although embodiments of the invention provide function, wherein only a part for finite element mesh is by symmetrical
Constraint, embodiments of the invention are not limited to such method.Figure 10 depicts finite element mesh 1000, wherein whole grid by
To constraint.As depicted in Figure 10, left half 1001 and right half 1002 are by the symmetry constraint on plane 1003.
Symmetry constraint can also be defined by plane and one group of face through connection.In such embodiments, it can then know
Other inter-engagement point is to retrieve individually symmetrical area.Also further, embodiment can recognize symmetrical area using plane,
Wherein the plane can be defined by the element (such as summit, face and/or edge) of grid.Although describing for defining symmetrically about
The various difference in functionalitys of beam, but embodiment can use these functions in any combinations.In addition it is possible to use identical or different
The selected face of institute of group to constrain for mesh definition.
Embodiment can also include ensuring that there is correspondence between the summit, edge and/or face by symmetry constraint
Function.One such exemplary embodiment depends on the recursive algorithm of the topological structure based on grid to determine correspondence.
In embodiment, this is performed by the profile in each symmetrical area of analysis.Such example, wherein grid are depicted in fig. 11
1100 are analyzed to confirm the correspondence between the summit, edge and face suffered restraints.Such embodiment is from the side of profile
Edge 1101 starts, and recognizes adjacent circulation 1102 from network.From circulation 1102 and circulation 1102 orientations in, summit and
Edge is retrieved and paired together with correct order.Once circulation 1102 is processed, such method is just then moved
Recognize to subsequent cycle 1103 and similarly summit and edge.This is performed on the both sides of grid 1100, and once two
The all elements in region are processed, and method just stops and all elements are paired.By this way, because finite element mesh
The edge contour and boundary face of confining region are associated, so this two groups face (that is, the sides of constraint and constraint through connection
Opposite side) all elements be 2 to multiply 2 ground and be associated in neighbour propagates.In addition, when making such determine, in engagement
Element (for example, symmetry of plane) on point can be the symmetry elements of its own, but in such embodiments, select face
It is not left in the case of no plane of symmetry.
Pair for each element (face, edge or summit) that embodiments of the invention also are stored in included in each symmetrical area
Ying Xing.This realizes the ability of across the symmetrical plane application modification (for example, from right to left and from left to right) in the two directions.Constraint
Stored in an efficient way, to allow to perform all scenario, and the present invention can pass through any species to grid
Modification maintain two symmetrical area definitions.This means all modifications by subdivided meshes come keep two groups of faces, edge and/
Or summit.In certain embodiments, each side of the profile on the right side, the profile on the left side and right and left profile can also be stored
The boundary face of edge.The other details on above-mentioned storage is described on Figure 12.
Embodiments of the invention can utilize the uniquely tagged system of the element for recognizing finite element mesh.Figure 12 is retouched
Such exemplary indicia system on the finite element mesh 1220a with mark 1220b is painted.In embodiment
In, face and summit can be recognized using mark (such as digital) within a grid.Figure 12 is depicted with the unique of identification summit
The grid 1220b of numeral.Face can be similarly labeled.Demarcated for example, can be recognized with mark 17 by summit 5,6,7 and 8
Face 1221.In another embodiment, the summit (such as 5,6,7,8) demarcated to face can be used to recognize face.Similarly, side
Edge can be identified using unique identifier or edge can be recognized by their two apex markers.For example, edge
1222 can be identified as edge (1,2).
In the exemplified embodiment, right wheel relevant with (5,8,4,1) with summit (11,12,9,10) respectively is stored
Exterior feature 1223 and left profile 1224.Similarly, the embodiment can complete identical thing to the relative edge interface of these profiles.This
The embodiment of invention can also store the symmetrical summit of each pair and each pair plane of symmetry.For example, all pairs of symmetrical top can be stored
Point (7,13), (6,16), (3,14), (2,15), (8,12), (5,11), (4,9) and (1,10).It can also store except other faces
The plane of symmetry in addition, such as face (17,19), 1221 and 1225.Embodiment can use unique identifier to each edge, or often
Individual edge can be recognized by its corresponding apex marker.For example, left profile includes edge (5,8), edge (8,4), edge (4,1)
With edge (1,5), and right wheel exterior feature include edge (11,12), edge (12,9), edge (9,10) and edge (10,11).
Figure 13 shows the symmetry transformation using the principle according to embodiment.In fig. 13, grid 1330 is let it is assumed that
With the symmetry transformation defined according to principle specifically described herein.Start, mobile 1332 left summits 1331.Then, find symmetrical
Right summit 1333.This summit for example can be determined by the use of unique apex marker system specifically described herein.This
Outside, symmetrical summit can have previously been stored to (1331,1333), thus the identification on summit 1333 is become effective.In addition, finding top
The barycenter 1335 of point 1331 and 1333.This can be determined according to any principle being known in the art.In addition, summit 1331
It can also be identified as through barycenter 1335 and be orthogonal on summit 1331 with 1333 midplane (that is, mid-plane) 1336
And the plane in the direction between 1333.According to embodiment, any method being known in the art can be used to determine centre
Plane and barycenter.It is, for example, possible to use equationTo determine barycenter.And then, midplane 1336 will be used and right
The symmetric manipulator 1334 for claiming motion 1334 to be inferred to is applied to the symmetrical summit found using the symmetry constraint of previous definition
1333。
Figure 13 show with reference to symmetry constraint come it is using so that the easy vertex manipulation of design variation to grid one
Individual example, wherein symmetry are needed (at least on one part).These principles can apply to all other summit behaviour
Vertical (rotation, attract, move, moved along normal along grid lines), by by these manipulations be thought of as from starting position to
The translation of final position.For example, edge rotation can be taken as the translation on two summits at edge.
Embodiments of the invention allow user rapidly and easyly to create with some parts corresponding to grid or complete
Grid symmetrical area 3D subdivision surfaces.This can greatly reduce to perform and the design variation of finite element mesh is spent
Time.Figure 14 show constrain create when original finite element mesh 1440a and after design variation is performed
Grid 1440b example.In fig. 14, grid 1440a is defined as the symmetry constraint applied to whole grid 1440a.
When performing design variation on grid, they only need to be performed on the side of symmetry constraint by user again.Therefore, accelerate to set
Meter process is quickly to produce modified grid 1440b.In addition, this can accelerate to complete 3D CAD models 1441.
As described herein, the method for embodiments of the invention can be started with defining symmetry constraint.It can pass through
Selection user wants to be maintained the face in symmetrical symmetrical area to define symmetry constraint.After definition constraint, user can start
The modification of whole shape.Figure 15 shows grid 1550, wherein have selected the face defined by profile 1551.Give tacit consent to plane ZX
1552 are used to make the right side 1553 of constraint to be separated with the left side 1554 constrained.Selection face and recognize plane (this can include make
With acquiescence plane 1552) after, contour identification 1551 and 1555.In embodiment, it is selected to indicate that feedback is provided to user
The face and corresponding face selected can be identified, in order to create symmetrical area.In embodiment, Pop-up message or logical can be passed through
Cross and visually indicate and (for example highlight profile 1551 and 1555) to provide this feedback.When constraint is successfully created, often
The individual right side, edge and summit are by the similar left side, edge and summit with its own.In addition, embodiments of the invention can lead to
Cross any means as known in the art and further feedback is provided, to indicate to the user that constraint is successfully created.In addition, Shen
Ask someone it should be noted that, although term " left side " and " right side " has been used throughout the specification to describe plane with opposite side pair
Finite element on the side of title, but embodiment is not so limited, and embodiment can utilize fixed across any symmetrical plane
The symmetry constraint of justice.
Figure 16 A-C depict the example for the mesh modification that the principle of embodiment can be used symmetrically to perform.Figure 16 A describe
There is the grid 1660a of the symmetry constraint defined according to principle specifically described herein.In such exemplary embodiment, when
During mobile 1662 edge 1661, it may be determined that mobile 1662 symmetry transformation and symmetry displacement is applied to corresponding symmetrical edge
1663.Similarly, Figure 16 B depict grid 1660b, wherein mobile 1672 summits 1671, and symmetry displacement and then can be
It is performed on symmetrical summit 1673.Equally, Figure 16 C depict grid 1660c, wherein summit 1674 is shifted 1675, and it is right
Displacement is claimed to can apply to symmetrical summit 1676.
Figure 17 is the computer implemented method 1770 for being used to change finite element mesh according to an embodiment of the invention
Flow chart.When user starts in step 1772 by selection face, edge, summit and/or selection/definition symmetrical plane, side
Method 1770 starts 1771.User can use various methods to select face/edge/summit/plane.For example, by using mouse
Face is selected over the display.Alternatively, user can select face on the touchscreen or by input face mark or position.It is similar
Method can be used for plane selection and define.When plane is defined or is selected, method 1770 proceeds with step
1776 two profiles of identification.When being chosen face to face, then two of the face with free edge are determined whether there is in step 1773
The group of individual closing and separation.If not having the group of the two separation and closing of free edge, make in step 1774 acquiescence
Use plane ZX.If there is the group of two with free edge separation and closing, then step 1775 Mian Liangge areas it
Between midplane between calculating group.Proceeded by step 1773-1775 or step 1772 define plane after, side
Method 1770 continues to recognize two profiles of symmetry constraint in step 1776.Use the face and plane contour identification suffered restraints.Two
Individual profile is the contour line of the grid elements on the opposite side of symmetrical plane suffered restraints.In other words, according to embodiment,
Each profile corresponds to the free edge (edge of the only one of which plane of incidence) in the region by symmetry constraint.Figure 15 illustrates
And exemplary profile 1551 and 1551 is described above.It is true in step 1777 after step 1776 identifies profile
Determine all symmetrical right of summit, face and edge.Any method specifically described herein can be used (for example, above for figure
Neighbour's transmission method described in 11) recognized in step 1777 it is symmetrical right.And then, the profile recognized and step of step 1776
Symmetrical pair calculated of 1777 is then tested to determine whether correct constraint can be defined in step 1778 again.According to reality
Example is applied, test process browses the group on element (such as face, edge and summit), and determine whether each element has a pair.
The test of step 1778 determines whether there is two of two groups of boundary faces with the face, edge and summit for producing two similar groups
Profile.In other words, test determines whether each face, edge and summit have corresponding face, edge and summit.When meeting step
During 1778 condition, create and constrain in step 1779, when being unsatisfactory for condition, method 1770 restarts 1771.In replacement
In embodiment, user can not receive the test of failure and be identified as in test crash to element.
In an exemplary embodiment of the present invention, it have modified the mould of stored grid in the establishment of the constraint of step 1779
Type, but not the shape of modification grid.By this way, part of the constraint as original mesh.Therefore, profit can alternatively be recognized
With the grid of the principle of embodiment.For example, the element in asymmetric grid (face, edge or summit) can be by its asymmetric element
In the case of modification and/or the grid suffered restraints two symmetry elements together by modification in the case of, grid it is symmetrical
Property is likely to be broken.
Figure 18 is the computer based method that the grid with symmetry constraint is changed according to the principle of exemplary embodiment
1880 flow chart.Method 1880 starts 1881 and the element or multiple elements that determine to be changed and (for example moved) in step 1882
Whether there is symmetry.Because the embodiment of method 1880 allows user once to change multiple elements, in each symmetrical area
Each element of modification is tested to determine if with appropriate symmetry.This method restarts 1881, if often
Individual element does not have symmetry.However, when each chosen elements of each constraint have symmetry, being calculated often in step 1883
The symmetry transformation of individual element, and and then perform each symmetry transformation in step 1884.Original as known in the art can be used
Manage to calculate symmetry transformation.In addition, in embodiment, for the summit (or edge or face) of each modification, retrieving conversion T
(for example, mobile vector, transformation matrix, weighted value), and and then calculate Local Symmetric plane (midpoint put in pairs, from barycenter
The symmetrical plane of calculating and the normals defined by two paired points).Then, corresponding symmetry transformation (matrix) is applied to this original
Begin conversion T to calculate the symmetrical modification to be applied in paired element (summit or edge or face).
Figure 19 is the computer based system 1930 that can be used for performing mesh modification according to an embodiment of the invention
Simplified block diagram.System 1930 includes bus 1935.Bus 1935 is used as the interconnection between the various parts of system 1930.Even
Be connected to bus 1930 is to be used to connect various input and output devices (for example, keyboard, mouse, display, loudspeaker etc.)
To the input-output apparatus interface 1938 of system 1930.CPU (CPU) 1932 is connected to bus 1935 and provided
The execution of computer instruction.Memory 1937 provides the volatile storage of data for computer instructions.Memory 1936 is
Software instruction provides non-volatile memories, such as operating system (not shown).System 1930 also includes being used to be connected to this area
In known any kind of network (including wide area network (WAN) and Local Area Network)) network interface 1931.
It should be appreciated that exemplary embodiment specifically described herein can be realized with number of different ways.At some
In example, various methods specifically described herein and machine can be each by physics, virtual or mixed universal computer (for example, meters
Calculation machine system 1930) or computer network environment (for example, the computer environment 2000 described below in relation to Figure 20) realize.Can
To be performed for example by the way that software instruction is loaded into memory 1937 or non-volatile storage 1936 by CPU 1932
Computer system 1930 is converted to the machine for performing method (such as 660,1770 and/or 1880) specifically described herein.This
Those of ordinary skill in field is it will be further understood that system 1930 and its various parts can be configured as performing herein
Described any embodiment of the invention.In addition, system 1930 can be realized using operatively internally or being externally coupled to
Any combination of various embodiments specifically described herein of the hardware of system 1930, software and firmware module.
Figure 20, which is shown, can realize the computer network environment 2000 of embodiments of the invention.In computer network environment
In 2000, server 2001 is linked to client 2003a-n by communication network 2002.Environment 2000 can be used for allowing client
End 2003a-n individually or with server 2001 performs the above any method (for example, 660,1770 in combination
And/or 1880).
Embodiment or its aspect can be realized in the form of hardware, firmware or software.If realized in software,
Software, which can be stored in, to be configured as enabling a processor to being loaded into software or any non-transient computer of the subset of its instruction can
Read medium.The subsequent execute instruction of processor simultaneously is configured as operating or so that device is grasped in mode as described herein
Make.
In addition, firmware, software, routine or instruction can be described as performing herein some actions of data processor
And/or function.It should be appreciated, however, that the such description included herein is just for the sake of convenient and such dynamic
Make in fact by computing device, processor, controller or the miscellaneous equipment generation for performing firmware, software, routine, instruction etc..
It should be appreciated that flow chart, block diagram and network can include more or less elements, these elements are different
Arrange or be represented differently in ground.But it will be appreciated that some embodiments can specify that block and network and block and network
The quantity of figure, so as to show the execution of embodiment realized in a particular manner.
And hence it is also possible to another to realize with various computer architectures, physics, virtual, cloud computer and/or some of combination
Outer embodiment, and data processor therefore specifically described herein is intended to for illustration purposes only not as embodiment
Limitation.
Although the present invention is particularly shown and described by reference to its exemplary embodiment, those of skill in the art
It will be understood that, various changes can be made in form and details without departing from the model of the invention covered by appended claims
Enclose.
Claims (20)
1. a kind of method that finite element mesh of modification 3D models is represented, methods described includes：
The symmetry constraint of finite element mesh is defined by the user, the finite element mesh is the expression of main body 3D models, and
The symmetry constraint includes two asymmetric areas of the finite element mesh symmetrically to be changed；
Recognize the corresponding finite element between described two asymmetric areas；
The user performs behaviour at least one element in the corresponding finite element recognized in described two asymmetric areas
It is vertical；And
Symmetrically perform the manipulation on two or more corresponding finite elements for being recognized, described two or more
Finite element is identified as corresponding to state at least one finite element, wherein, symmetrically performing the manipulation causes described to have
Described two asymmetric areas of limit element grid are symmetrically changed, so as to represent the symmetrical modification in the main body 3D models.
2. according to the method described in claim 1, wherein, recognize the corresponding finite element bag between described two asymmetric areas
Include：
Recognize symmetrical edge, summit and the face in described two areas.
3. according to the method described in claim 1, wherein, symmetrically perform it is described manipulation include：
Determine Local Symmetric plane, the Local Symmetric plane by least one described finite element and described two or more
The barycenter of finite element is defined and perpendicular to by least one described finite element and two or more described finite elements
The direction of definition；
The symmetry transformation of the manipulation is calculated using the Local Symmetric plane；And
Calculated symmetry transformation is performed on two or more described finite elements.
4. according to the method described in claim 1, wherein, the symmetry constraint is only applied to the sub-portion of the finite element mesh
Point.
5. according to the method described in claim 1, wherein, define symmetry constraint include it is following at least one of：
Recognize first group of face and second group of face through connection through connection；
Recognize plane and one group of face through connection；
Recognize one group of face；And
Recognize plane.
6. according to the method described in claim 1, wherein, the finite element mesh is recognized using corresponding uniquely tagged
The element in described two asymmetric areas.
7. according to the method described in claim 1, wherein, defining the symmetry constraint includes：
Determine the separation shape between described two asymmetric areas.
8. method according to claim 7, wherein, the separation shape is plane.
9. method according to claim 7, wherein, it is described corresponding limited between described two asymmetric areas are recognized
The separation shape is used during element.
10. a kind of be used to change the computer system that the finite element mesh of 3D models is represented, the computer system includes：
Processor；And
Memory, it has the computer generation code instruction that is stored thereon, the processor and refers to the computer code
The memory of order is configured such that the system：
The symmetry constraint that finite element mesh is defined by the user is realized, the finite element mesh is the expression of main body 3D models,
And the symmetry constraint includes two asymmetric areas of the finite element mesh symmetrically to be changed；
Recognize the corresponding finite element between described two asymmetric areas；
Realize that the user holds at least one element in the corresponding finite element recognized in described two asymmetric areas
Row is manipulated；And
Symmetrically perform the manipulation on two or more corresponding finite elements for being recognized, described two or more
Finite element is identified as corresponding to state at least one finite element, wherein, symmetrically performing the manipulation causes described to have
Described two asymmetric areas of limit element grid are symmetrically changed, so as to represent the symmetrical modification in the main body 3D models.
11. system according to claim 10, wherein, the corresponding finite element between described two asymmetric areas are recognized
When plain, the processor and the memory with the computer generation code instruction are further configured such that the system：
Recognize symmetrical edge, summit and the face in described two areas.
12. system according to claim 10, wherein, when symmetrically performing the manipulation, the processor and have
The memory of the computer generation code instruction is further configured such that the system：
Determine Local Symmetric plane, the Local Symmetric plane by least one described finite element and described two or more
The barycenter of finite element is defined and perpendicular to by least one described finite element and two or more described finite elements
The direction of definition；
The symmetry transformation of the manipulation is calculated using the Local Symmetric plane；And
Calculated symmetry transformation is performed on two or more described finite elements.
13. system according to claim 10, wherein, the symmetry constraint is only applied to the son of the finite element mesh
Part.
14. system according to claim 10, wherein, when defining symmetry constraint, the processor and with the meter
The memory of calculation machine code command is further configured such that the system performs at least one in the following：
Recognize first group of face and second group of face through connection through connection；
Recognize plane and one group of face through connection；
Recognize one group of face；And
Recognize plane.
15. system according to claim 10, wherein, the finite element mesh is recognized using corresponding uniquely tagged
Described two asymmetric areas element.
16. system according to claim 10, wherein, when defining the symmetry constraint, the processor and with institute
The memory for stating computer generation code instruction is further configured such that the system：
Determine the separation shape between described two asymmetric areas.
17. system according to claim 16, wherein, the separation shape is plane.
18. system according to claim 16, wherein, described between described two asymmetric areas are recognized corresponding has
The separation shape is used when limiting element.
19. it is a kind of including the computer program production for the computer-readable instruction being stored in non-transitory computer-readable medium
Product, the computer-readable instruction to operate below the computing device in response to the execution of computing device, including：
The symmetry constraint of finite element mesh is defined by the user, the finite element mesh is the expression of main body 3D models, and
The symmetry constraint includes two asymmetric areas of the finite element mesh symmetrically to be changed；
Recognize the corresponding finite element between described two asymmetric areas；
The user performs behaviour at least one element in the corresponding finite element recognized in described two asymmetric areas
It is vertical；And
Symmetrically perform the manipulation on two or more corresponding finite elements for being recognized, described two or more
Finite element is identified as corresponding to state at least one finite element, wherein, symmetrically performing the manipulation causes described to have
Described two asymmetric areas of limit element grid are symmetrically changed, so as to represent the symmetrical modification in the main body 3D models.
20. computer program product according to claim 19, wherein, recognize the correspondence between described two asymmetric areas
Finite element include：
Recognize symmetrical edge, summit and the face in described two areas.
Applications Claiming Priority (4)
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| EP15307030.5A EP3182306A1 (en) | 2015-12-16 | 2015-12-16 | Topological change in a constrained asymmetrical subdivision mesh |
| EP15307029.7A EP3182378B1 (en) | 2015-12-16 | 2015-12-16 | Modification of a constrained asymmetrical subdivision mesh |
| EP15307030.5 | 2015-12-16 | ||
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| CN201611110095.8A Active CN107066646B (en) | 2015-12-16 | 2016-12-02 | Method, system, and medium for topology change in constrained asymmetric subdivision networks |
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| EP3961471A1 (en) | 2020-08-28 | 2022-03-02 | Siemens Industry Software NV | Modifying a finite element mesh |
| US20240087173A1 (en) * | 2022-09-14 | 2024-03-14 | Tencent America LLC | Base mesh coding by using surface reflection symmetry |
| US20240127490A1 (en) * | 2022-09-26 | 2024-04-18 | Tencent America LLC | Connectivity coding for symmetry mesh |
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| CN107066646B (en) | 2022-04-12 |
| JP6892257B2 (en) | 2021-06-23 |
| JP2017111821A (en) | 2017-06-22 |
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| CN107066646A (en) | 2017-08-18 |
| US10311182B2 (en) | 2019-06-04 |
| US10289771B2 (en) | 2019-05-14 |
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| JP2017111820A (en) | 2017-06-22 |
| JP6892256B2 (en) | 2021-06-23 |
| CN106991204B (en) | 2022-01-14 |
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